Fluid and Particle Motion in Turbulent Stirred Tanks. Particle Motion

The two-scale turbulence concept is recommended for modeling the turbulence in a baffled vessel equipped with a Rushton-type turbine impeller. A three-equation isotropic turbulence model is proposed that employs the balance equations for: the kinetic energy of the large scale vortices; the kinetic energy of the inertial subrange eddies; and the dissipation rate of the small-scale turbulence. The energy transfer rate from the large-scale vortices is prescribed algebraically. Flow patterns are modeled by solving the transport equations for vorticity, stream function, and tangential momentum. The Reynolds stresses are modeled by means of the effective viscosity, based on the three-equation model of turbulence. The calculated profiles of the mean velocity at the tank wall agree with experimental data obtained in the same system by means of a Pitot tube.established a model to describe turbulent flow in the impeller region for a Rushton-type turbine impeller. The method commonly used to predict velocity fields in turbulent flows is based upon the concept of turbulent viscosity, which is evaluated from the local values of overall kinetic energy of turbulence k and its dissipation rate t. Balance equations of turbulent quantities must be solved simultaneously with the balance equations for mass and the mean momentum. Applied ad hoc to the mixing vessel, the k-6 model fails to give acceptable results of the turbulence parameters in mixing vessels, as indicated in the results of Platzer (1981). The approach applied here extends the classic k-c model to include the turbulence energy scales k, and kT, where the former represents the production-scale vortices and the latter represents the inertial range eddies. The extended model is employed here to construct an algorithm for the computation of profiles of mean velocity, kinetic energy of turbulence, and dissipation rate of turbulence.The model is compared with experimental data to evaluate the reliability of the numerical predictions. The numerical results for the mean velocity profiles in the wall region are compared with experimentally measured velocities for a laboratorysize vessel. The wall region presents many distinct advantages in measurements for validation of this model. These include verification of the secondary circulation, sufficiently high mean velocities for satisfactory accuracy, moderate levels of turbulence, and a check in the region where the assumption of axial symmetry may be violated. Wall measurements are preferable to impeller measurements because of large degrees of anisotropy

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“…Considering the representative value of 6 given by Schwartzberg and Treybal (1968) as 6 = 0.3, Eq. 24 yields Av = 10.1%.…”

Section: Av =mentioning

confidence: 99%

Turbulent flow in stirred tanks. Part II: A two‐scale model of turbulence

et al. 1986

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“…[26] Schwartzberg and Treybal [26] suggested that in systems where the power number is a constant, the average energy dissipation rate is proportional to N 3 i D 5 =T 2 H in which N i is the impeller speed (rpm), D is the impeller diameter (cm), T is the tank diameter (cm), and H is the depth of liquid fills in tank (cm). The average energy dissipation rate (" o ) is taken to be equal to the power consumption rate per unit mass of mixing fluid and was obtained in an experiment using the standard cylindrical stirred water tank by Schwartzberg and Treybal.…”

Section: Mathematical Modelmentioning

confidence: 99%

Removal Dynamics of Airborne Road Dust in a Ventilated Airspace

Liao

Huang

Chen

et al. 2002

Journal of Environmental Science and Health, Part A

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We derive a simple linear dynamic equation to describe the removal mechanisms of airborne road dust from a ventilated airspace. The dynamic equation is sufficiently to take into account the simultaneous removal effects of turbulent coagulation, turbulent diffusive deposition, gravitational sedimentation, and airflow pattern within a ventilated airspace. Three dimensionless parameters TC, TD, and GS that characterize the relative effects of turbulent coagulation, turbulent diffusive deposition and gravitational settling, respectively, in a ventilated airspace were introduced to generalize the removal dynamics of airborne road dust. An environmental chamber test was carried out not only to determine the particle size distributions but also to verify the removal dynamics of airborne road dust in a ventilated airspace. Our results demonstrate that there is no significant variation for particle size distributions of road dust obtained from urban and suburban areas in north Taiwan region and both followed a lognormal distribution with average geometric mean diameter of 1.08 +/- 0.02 microm and geometric standard deviation of 2.59+/-0.03. Measured values match the simulated values with an r2 value of 0.93, whereas the overall RMSE value of 2.36 +/- 1.05 mg m(-3) is low, indicating that the ability to predict the removal dynamics of airborne road dust within a ventilated airspace using an average particle size based linear equation. Effects of TC, TD, GS, and various ventilation systems on the time-dependent road dust concentrations are also justified.

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“…Insbesondere in der Feststoffverfahrenstechnik, wo verstarkt der Wunsch nach Grundlagenwissen besteht, konnte die MR-Tomographie in Zukunft eine wichtige Rolle spielen. ac, [12] berechnen: (9) Fur die noch fehlende Taylorsche MikrogroBe 1, gilt nach Taylor [13] Axialriihrer zuriickzufiihren ist [5]. Auch das berechnete Konzentrationsprofil gibt diesen Verlauf wieder.…”

Section: Fazit Und Perspektivenunclassified